A ray OP of monochromatic light is incident on the face AB of prism ABCD mear vertex B at an incident angle of `60degree` (see figure). If the refractive index of the material of the prism is `sqrt3`, which of the following is (are) are correct? `

Options

A. The ray gets totally internally reflected at face `CD`
B. The ray comes out through face `AD`
C. The angle between the incident ray and the emergent rays is `90^(@)`
D. The angle between the incident ray and the emergent ray is `120^(@)`

Answer

A, B, C

Explanation

Critical angle of material of prism, `C = sin^(-1)((1)/(mu)) = sin^(-1)((1)/(sqrt(3)))`

For refraction at face `AB`.
`mu = (sin 60^(@))/(sin r)` or `sin r = (sin 60^(@))/(mu) = (sqrt(3) //2)/(sqrt(3)) = (1)/(2)`
`r = 30^(@)`
`:. /_BPQ = 90^(@) + 30^(@) = 120^(@)`
Hence, refracted ray goes along `PQ`. It meets the face `CD` at angle of incidence `= 45^(@)`.
As `"sin"^(-1)(1)/(sqrt(2)) gt "sin"^(-1)(1)/(sqrt(3))`
therefore, the ray `PQ` meets the face `CD` at an angle of incidence greater than critical angle. Hence, total internal reflection takes place at face `CD` of prism. The ray goes along `QR` and meets the face `DA` at an angle of incidence `30^(@)`. The emergent ray `RT` will go making an angle of emergence `60^(@)`. The incident ray `OP` and emergent ray `RT` will be inclined at an angle `90^(@)`.
Choice (a, b, c) are correct.